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 A200838 T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases 12
 8, 25, 16, 56, 69, 32, 105, 194, 191, 64, 176, 435, 676, 529, 128, 273, 846, 1817, 2356, 1465, 256, 400, 1491, 4108, 7587, 8210, 4057, 512, 561, 2444, 8239, 19930, 31677, 28610, 11235, 1024, 760, 3789, 15128, 45465, 96690, 132263, 99700, 31113, 2048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....8.....25......56......105.......176........273........400.........561 ...16.....69.....194......435.......846.......1491.......2444........3789 ...32....191.....676.....1817......4108.......8239......15128.......25953 ...64....529....2356.....7587.....19930......45465......93472......177381 ..128...1465....8210....31677.....96690.....250913.....577660.....1212729 ..256...4057...28610...132263....469116....1384813....3570086.....8291391 ..512..11235...99700...552247...2276028....7642875...22063924....56687801 .1024..31113..347434..2305835..11042700...42181611..136360286...387572529 .2048..86161.1210736..9627715..53576350..232803603..842739040..2649819955 .4096.238605.4219166.40199277.259938722.1284861277.5208328180.18116728573 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical for columns: k=1: a(n) = 2*a(n-1) k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) k=3: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4) k=4: a(n) = 5*a(n-1) -4*a(n-2) +3*a(n-3) -3*a(n-4) +a(n-5) -a(n-6) k=5: a(n) = 6*a(n-1) -6*a(n-2) +3*a(n-3) -5*a(n-4) +3*a(n-5) -2*a(n-6) +a(n-7) k=6: a(n) = 7*a(n-1) -9*a(n-2) +6*a(n-3) -9*a(n-4) +7*a(n-5) -7*a(n-6) +5*a(n-7) -2*a(n-8) +a(n-9) k=7: a(n) = 8*a(n-1) -12*a(n-2) +6*a(n-3) -10*a(n-4) +12*a(n-5) -11*a(n-6) +11*a(n-7) -6*a(n-8) +3*a(n-9) -a(n-10) Empirical for rows: n=1: a(k) = (2/3)*k^3 + 3*k^2 + (10/3)*k + 1 n=2: a(k) = (5/12)*k^4 + (19/6)*k^3 + (79/12)*k^2 + (29/6)*k + 1 n=3: a(k) = (4/15)*k^5 + (17/6)*k^4 + (28/3)*k^3 + (73/6)*k^2 + (32/5)*k + 1 n=4: a(k) = (61/360)*k^6 + (93/40)*k^5 + (779/72)*k^4 + (521/24)*k^3 + (1801/90)*k^2 + (239/30)*k + 1 n=5: a(k) = (34/315)*k^7 + (163/90)*k^6 + (1981/180)*k^5 + (557/18)*k^4 + (7807/180)*k^3 + (1361/45)*k^2 + (333/35)*k + 1 n=6: a(k) = (277/4032)*k^8 + (1375/1008)*k^7 + (4933/480)*k^6 + (2723/72)*k^5 + (14161/192)*k^4 + (11197/144)*k^3 + (216211/5040)*k^2 + (929/84)*k + 1 n=7: a(k) = (124/2835)*k^9 + (1123/1120)*k^8 + (244/27)*k^7 + (1991/48)*k^6 + (57133/540)*k^5 + (74183/480)*k^4 + (291427/2268)*k^3 + (9739/168)*k^2 + (568/45)*k + 1 EXAMPLE Some solutions for n=4 k=3 ..1....2....3....0....1....1....2....1....3....3....3....1....2....0....1....1 ..0....0....0....2....1....0....3....3....1....3....0....3....2....3....1....0 ..0....0....2....2....0....3....0....0....1....2....1....3....2....0....1....1 ..3....0....1....3....3....3....3....2....1....2....0....1....2....0....0....1 ..3....3....3....0....3....0....1....2....1....1....3....3....3....2....2....3 ..1....3....2....0....1....3....3....2....2....1....0....1....2....1....1....0 CROSSREFS Column 1 is A000079(n+2) Column 2 is A098182(n+3) Row 1 is A131423(n+1) Sequence in context: A023056 A103954 A217012 * A302160 A122984 A254341 Adjacent sequences: A200835 A200836 A200837 * A200839 A200840 A200841 KEYWORD nonn,tabl AUTHOR R. H. Hardin Nov 23 2011 STATUS approved

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Last modified March 21 19:39 EDT 2023. Contains 361410 sequences. (Running on oeis4.)